Branch-depth: Generalizing tree-depth of graphs
DC Field | Value | Language |
---|---|---|
dc.contributor.author | DeVos,Matt | - |
dc.contributor.author | Kwon, O jung | - |
dc.contributor.author | Oum, Sang-il | - |
dc.date.accessioned | 2023-08-22T03:11:07Z | - |
dc.date.available | 2023-08-22T03:11:07Z | - |
dc.date.created | 2023-07-19 | - |
dc.date.issued | 2020-12 | - |
dc.identifier.issn | 0195-6698 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189493 | - |
dc.description.abstract | We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns closely with the notions of tree-depth and shrub-depth of graphs as follows. For a graph G = (V, E) and a subset A of E we let lambda(G)(A) be the number of vertices incident with an edge in A and an edge in E \ A. For a subset X of V, let rho(G)(X) be the rank of the adjacency matrix between X and V \ X over the binary field. We prove that a class of graphs has bounded tree-depth if and only if the corresponding class of functions lambda(G) has bounded branch depth and similarly a class of graphs has bounded shrub-depth if and only if the corresponding class of functions rho(G) has bounded branch-depth, which we call the rank-depth of graphs.,Furthermore we investigate various potential generalizations of tree-depth to matroids and prove that matroids representable over a fixed finite field having no large circuits are well-quasi ordered by restriction. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD | - |
dc.title | Branch-depth: Generalizing tree-depth of graphs | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kwon, O jung | - |
dc.identifier.doi | 10.1016/j.ejc.2020.103186 | - |
dc.identifier.scopusid | 2-s2.0-85087922057 | - |
dc.identifier.wosid | 000565160300001 | - |
dc.identifier.bibliographicCitation | EUROPEAN JOURNAL OF COMBINATORICS, v.90, pp.1 - 23 | - |
dc.relation.isPartOf | EUROPEAN JOURNAL OF COMBINATORICS | - |
dc.citation.title | EUROPEAN JOURNAL OF COMBINATORICS | - |
dc.citation.volume | 90 | - |
dc.citation.startPage | 1 | - |
dc.citation.endPage | 23 | - |
dc.type.rims | ART | - |
dc.type.docType | 정기학술지(Article(Perspective Article포함)) | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | Y | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | MONADIC 2ND-ORDER LOGIC | - |
dc.subject.keywordPlus | RANK-WIDTH,MINORS | - |
dc.identifier.url | https://www.sciencedirect.com/science/article/pii/S0195669820301074?via%3Dihub | - |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
222, Wangsimni-ro, Seongdong-gu, Seoul, 04763, Korea+82-2-2220-1365
COPYRIGHT © 2021 HANYANG UNIVERSITY.
Certain data included herein are derived from the © Web of Science of Clarivate Analytics. All rights reserved.
You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.